Gravitational Attractive Force Between Sun and Earth

[bjphoenix]

It is Dietzgen slide rule. Something like this.

https://www.ebay.com/itm/1263115398...T40ghdhRTC&var=&widget_ver=artemis&media=COPY

In high school I used a metal slide rule made by Picket called the "Texas Speed Rule" for use in UIL competition. When I started college I bought a new model that had more log scales on it. The classic slide rules were the bamboo models with ivory plastic scales made by K&E and Post. In more recent years I've bought a few of those on ebay to add to my collection just for the nostalgia.

 

[Orestes Mayo]

My child, Naomi, was working on a homework problem in their Astronomy for non-science majors class in college. They texted me about it.

The problem involved the gravitational force between the Sun and Earth and between the Sun and Mars.

The problem, which I won’t go into here unless someone wants me to, got me to thinking. What IS the gravitational force between the Sun and the Earth? It can’t be that hard to calculate, right? It is some sort of application of the “inverse square law”, right?

So I looked up Newton’s gravitational attraction equation for the gravitational attraction between any two objects. It is an application of Newton’s second law of motion, Force = mass * acceleration.

The equation is F = G ((Mm)/r^2)

The equation is not hard to do with pencil and paper. The hardest part is remembering how to multiply and divide using scientific notation. The second hardest part is keeping the complicated units of each value straight.

Here it is.

View attachment 629524

So, anybody who knows middle school math can run this equation.

Thank you, Sir Isaac!

You get an A+ Well done.

BTW, Physicist here

 

[jqavins]

I think I was calculating the force at the point in space where the force the Sun exerts on Earth (call it F1) is equal to the force the Earth exerts on the Sun (call it F2).

No, because that would be everywhere. The force of gravity exerted on A by B is GM_AM_B/R². The force of gravity exerted on B by A is GM_BM_A/R². I trust you can see that those are the same, no matter where in space A and B are.

It should be noted that the answer is correct only if R is constant. Since Earth's orbit is not quite circular, R is not constant, so the real answer is dependent on where Earth is in its orbit.

Now find the velocities required for Earth and Mars to stay in their orbits.

Easy. Since we know that Earth and Mars do stay in their orbits, their observed orbital speeds are the speeds required. The speed is the orbit's circumference divided by one year. Using the same approximation that R is constant, for Earth that's 2×π×92,955,807.3 miles ÷ 8766 hours ≈ 66,656 mph. I'll leave that computation for Mars to someone who cares.

 

[Antares JS]

I've read a few things about chat gpt, it seems that the way it is trained it might have inaccurate information sometimes. It isn't intended to be an encyclopedia.

A lawyer in New York (I think) got in big trouble because he tried to use ChatGPT to do his research and it actually made up fake cases, and he didn't check ChatGPT's work and submitted documents to a judge citing precedents that didn't exist.

 

[bjphoenix]

A lawyer in New York (I think) got in big trouble because he tried to use ChatGPT to do his research and it actually made up fake cases, and he didn't check ChatGPT's work and submitted documents to a judge citing precedents that didn't exist.

I scroll facebook a little bit, there is actually some rocket content on there, and lots of photos come up that I'm sure are AI generated such as swimsuit photos of celebrities. They seem pretty easy to spot because they are too perfect. OTOH I've seen photos of other things such as firearms that look like they are real photos of real things but you can tell by the thing in the photo that no such item exists. I wonder if these are chatGPT fabrications.

 

[jqavins]

Does ChatGPT do pictures? It's a chatbot. There are other generative AI systems that make pictures.

 

[NTP2]

It's a chatbot.

Well technically (the best sentence start) it’s a large language model. But it’s basically the same thing.

 

[NTP2]

I'll leave that computation for Mars to someone who cares.

I get 62164km/h with the same method. With 1.5 as the mars year and 1.5 AU as radius.